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Cubature on Wiener space: pathwise convergence

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  • Christian Bayer
  • Peter K. Friz

Abstract

Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models. We give a random walk interpretation of cubature and similar (e.g. the Ninomiya--Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.

Suggested Citation

  • Christian Bayer & Peter K. Friz, 2013. "Cubature on Wiener space: pathwise convergence," Papers 1304.4623, arXiv.org.
    • Handle: RePEc:arx:papers:1304.4623
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    References listed on IDEAS

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    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Christian Litterer & Terry Lyons, 2007. "Cubature on Wiener Space Continued," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 12, pages 197-217, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Lopusanschi, Olga & Simon, Damien, 2018. "Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2404-2426.

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